Question

Evaluate ∫ tan³x sec⁴x dx

Answer 1

∫ tan³x sec⁴x dx

In this integral we will use the formula,

1+tan²x = sec²x

Then equation will be transform in below form-

I = ∫tan³x sec²x sec²x dx 

= ∫tan³x (1 + tan²x) sec²x dx 

Now,

Put tanx = t which means sec²xdx = dt,

Now,

Put the value of t, which is t = tanx in above integral

I = \(\frac{tan^5x}{5}\)+\(\frac{tan^6x}{6}\)